%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP001+6 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:29:51 PM UTC 2026
% Result : Theorem 3.13s 1.07s
% Output : CNFRefutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 48 ( 19 unt; 0 def)
% Number of atoms : 211 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 254 ( 91 ~; 82 |; 66 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 243 ( 0 sgn 225 !; 18 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ! [X1] : product(inverse(X1),X1,X0)
& ! [X1] : product(X1,inverse(X1),X0)
& ! [X1] : product(X0,X1,X1)
& ! [X1] : product(X1,X0,X1)
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X5,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X4,X3,X6) )
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X4,X3,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X1,X5,X6) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3) )
=> ( ! [X1] : product(X1,X1,X0)
=> ! [X4,X5,X6] :
( product(X4,X5,X6)
=> product(X5,X4,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ! [X1] : product(inverse(X1),X1,X0)
& ! [X1] : product(X1,inverse(X1),X0)
& ! [X1] : product(X0,X1,X1)
& ! [X1] : product(X1,X0,X1)
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X5,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X4,X3,X6) )
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X4,X3,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X1,X5,X6) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3) )
=> ( ! [X1] : product(X1,X1,X0)
=> ! [X4,X5,X6] :
( product(X4,X5,X6)
=> product(X5,X4,X6) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ! [X0] :
( ( ! [X19] : product(inverse(X19),X19,X0)
& ! [X18] : product(X18,inverse(X18),X0)
& ! [X17] : product(X0,X17,X17)
& ! [X16] : product(X16,X0,X16)
& ! [X10,X11,X12,X13,X14,X15] :
( ( product(X10,X14,X15)
& product(X11,X12,X14)
& product(X10,X11,X13) )
=> product(X13,X12,X15) )
& ! [X4,X5,X6,X7,X8,X9] :
( ( product(X7,X6,X9)
& product(X5,X6,X8)
& product(X4,X5,X7) )
=> product(X4,X8,X9) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3) )
=> ( ! [X20] : product(X20,X20,X0)
=> ! [X21,X22,X23] :
( product(X21,X22,X23)
=> product(X22,X21,X23) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
? [X0] :
( ! [X19] : product(inverse(X19),X19,X0)
& ! [X18] : product(X18,inverse(X18),X0)
& ! [X17] : product(X0,X17,X17)
& ! [X16] : product(X16,X0,X16)
& ! [X10,X11,X12,X13,X14,X15] :
( ~ product(X10,X14,X15)
| ~ product(X11,X12,X14)
| ~ product(X10,X11,X13)
| product(X13,X12,X15) )
& ! [X4,X5,X6,X7,X8,X9] :
( ~ product(X7,X6,X9)
| ~ product(X5,X6,X8)
| ~ product(X4,X5,X7)
| product(X4,X8,X9) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3)
& ! [X20] : product(X20,X20,X0)
& ? [X21,X22,X23] :
( product(X21,X22,X23)
& ~ product(X22,X21,X23) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
? [X0] :
( ! [X19] : product(inverse(X19),X19,X0)
& ! [X18] : product(X18,inverse(X18),X0)
& ! [X17] : product(X0,X17,X17)
& ! [X16] : product(X16,X0,X16)
& ! [X10,X11,X12,X13,X14,X15] :
( ~ product(X10,X14,X15)
| ~ product(X11,X12,X14)
| ~ product(X10,X11,X13)
| product(X13,X12,X15) )
& ! [X4,X5,X6,X7,X8,X9] :
( ~ product(X7,X6,X9)
| ~ product(X5,X6,X8)
| ~ product(X4,X5,X7)
| product(X4,X8,X9) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3)
& ! [X20] : product(X20,X20,X0)
& ? [X21,X22,X23] :
( product(X21,X22,X23)
& ~ product(X22,X21,X23) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
? [X0] :
( ! [X23] : product(inverse(X23),X23,X0)
& ! [X22] : product(X22,inverse(X22),X0)
& ! [X21] : product(X0,X21,X21)
& ! [X20] : product(X20,X0,X20)
& ! [X14,X15,X16,X17,X18,X19] :
( ~ product(X14,X18,X19)
| ~ product(X15,X16,X18)
| ~ product(X14,X15,X17)
| product(X17,X16,X19) )
& ! [X8,X9,X10,X11,X12,X13] :
( ~ product(X11,X10,X13)
| ~ product(X9,X10,X12)
| ~ product(X8,X9,X11)
| product(X8,X12,X13) )
& ! [X5,X6] :
? [X7] : product(X5,X6,X7)
& ! [X4] : product(X4,X4,X0)
& ? [X1,X2,X3] :
( product(X1,X2,X3)
& ~ product(X2,X1,X3) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ! [X23] : product(inverse(X23),X23,sK0)
& ! [X22] : product(X22,inverse(X22),sK0)
& ! [X21] : product(sK0,X21,X21)
& ! [X20] : product(X20,sK0,X20)
& ! [X14,X15,X16,X17,X18,X19] :
( ~ product(X14,X18,X19)
| ~ product(X15,X16,X18)
| ~ product(X14,X15,X17)
| product(X17,X16,X19) )
& ! [X8,X9,X10,X11,X12,X13] :
( ~ product(X11,X10,X13)
| ~ product(X9,X10,X12)
| ~ product(X8,X9,X11)
| product(X8,X12,X13) )
& ! [X5,X6] : product(X5,X6,sK4(X5,X6))
& ! [X4] : product(X4,X4,sK0)
& product(sK1,sK2,sK3)
& ~ product(sK2,sK1,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X7,sK4(X5,X6))],[f6]) ).
fof(f10,plain,
! [X21] : product(sK0,X21,X21),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X20] : product(X20,sK0,X20),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X18,X19,X16,X14,X17,X15] :
( ~ product(X14,X18,X19)
| ~ product(X15,X16,X18)
| ~ product(X14,X15,X17)
| product(X17,X16,X19) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X10,X11,X8,X9,X12,X13] :
( ~ product(X11,X10,X13)
| ~ product(X9,X10,X12)
| ~ product(X8,X9,X11)
| product(X8,X12,X13) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X6,X5] : product(X5,X6,sK4(X5,X6)),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X4] : product(X4,X4,sK0),
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
product(sK1,sK2,sK3),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
~ product(sK2,sK1,sK3),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
~ product(sK2,sK1,sK3),
inference(cnf_transformation,[],[f17]) ).
tcf(c_50,negated_conjecture,
product(sK1,sK2,sK3),
inference(cnf_transformation,[],[f16]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] : product(X0,X0,sK0),
inference(cnf_transformation,[],[f15]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] : product(X0,X1,sK4(X0,X1)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X2,X5,X4)
| ~ product(X1,X5,X3)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_55,negated_conjecture,
! [X0: $i] : product(X0,sK0,X0),
inference(cnf_transformation,[],[f11]) ).
tcf(c_56,negated_conjecture,
! [X0: $i] : product(sK0,X0,X0),
inference(cnf_transformation,[],[f10]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(sK2,sK1,sK3)
| ~ product(X1,sK1,X2)
| ~ product(X0,X2,sK3)
| ~ product(X0,X1,sK2) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X2,X3,sK1)
| ~ product(X0,X4,sK1)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_102,plain,
product(sK1,sK0,sK1),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X0,X4,sK2)
| ~ product(X2,X3,sK2)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_113,plain,
product(sK0,sK2,sK2),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X1,sK1)
| ~ product(sK1,sK0,sK1)
| ~ product(sK1,X0,X2)
| ~ product(X0,X1,sK0) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X2,sK2)
| ~ product(sK0,sK2,sK2)
| ~ product(X1,sK2,X2)
| ~ product(X0,X1,sK0) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X2,X3,sK3)
| ~ product(X0,X4,sK3)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_182,plain,
product(sK3,sK0,sK3),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(sK1,X1,X2)
| ~ product(sK3,X0,X2)
| ~ product(sK2,X0,X1) ),
inference(superposition,[status(thm)],[c_50,c_53]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X0,X4,X3)
| ~ product(X1,X2,X4)
| ~ product(sK4(X0,X1),X2,X3) ),
inference(superposition,[status(thm)],[c_52,c_53]) ).
tcf(c_321,plain,
product(sK1,sK1,sK0),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_337,plain,
! [X0: $i] :
( product(sK3,X0,sK1)
| ~ product(sK1,sK0,sK1)
| ~ product(sK1,sK2,sK3)
| ~ product(sK2,X0,sK0) ),
inference(instantiation,[status(thm)],[c_151]) ).
tcf(c_446,plain,
! [X0: $i] :
( product(X0,sK3,sK2)
| ~ product(sK0,sK2,sK2)
| ~ product(sK1,sK2,sK3)
| ~ product(X0,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_161]) ).
tcf(c_449,plain,
product(sK2,sK2,sK0),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_548,plain,
( product(sK3,sK2,sK1)
| ~ product(sK1,sK0,sK1)
| ~ product(sK1,sK2,sK3)
| ~ product(sK2,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_557,plain,
! [X0: $i,X1: $i] :
( product(sK1,sK4(sK2,X0),X1)
| ~ product(sK3,X0,X1) ),
inference(superposition,[status(thm)],[c_52,c_190]) ).
tcf(c_605,plain,
( product(sK1,sK3,sK2)
| ~ product(sK0,sK2,sK2)
| ~ product(sK1,sK1,sK0)
| ~ product(sK1,sK2,sK3) ),
inference(instantiation,[status(thm)],[c_446]) ).
tcf(c_995,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X1,sK3)
| ~ product(sK3,sK0,sK3)
| ~ product(sK3,X0,X2)
| ~ product(X0,X1,sK0) ),
inference(instantiation,[status(thm)],[c_180]) ).
tcf(c_1484,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X2,sK0)
| ~ product(X0,sK4(X1,X0),X2) ),
inference(superposition,[status(thm)],[c_51,c_192]) ).
tcf(c_2443,plain,
! [X0: $i] :
( product(sK2,sK1,sK3)
| ~ product(sK1,sK3,sK2)
| ~ product(sK3,sK1,X0)
| ~ product(sK1,X0,sK3) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_2469,plain,
! [X0: $i] :
( product(sK2,X0,sK0)
| ~ product(sK3,sK1,X0) ),
inference(superposition,[status(thm)],[c_557,c_1484]) ).
tcf(c_3933,plain,
! [X0: $i] :
( product(sK1,X0,sK3)
| ~ product(sK3,sK0,sK3)
| ~ product(sK3,sK2,sK1)
| ~ product(sK2,X0,sK0) ),
inference(instantiation,[status(thm)],[c_995]) ).
tcf(c_4563,plain,
! [X0: $i] : ~ product(sK3,sK1,X0),
inference(global_subsumption_just,[status(thm)],[c_2469,c_50,c_49,c_102,c_113,c_182,c_321,c_449,c_548,c_605,c_2443,c_2469,c_3933]) ).
tcf(c_4566,plain,
$false,
inference(superposition,[status(thm)],[c_52,c_4563]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP001+6 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 13:10:37 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.32
% 0.03/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.32
% 0.03/0.32 % Detected problem language: tptp
% 0.06/0.33 % Proving...
% 3.13/1.07 % SZS status Started for theBenchmark.p
% 3.13/1.07 % SZS status Theorem for theBenchmark.p
% 3.13/1.07
% 3.13/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.13/1.07
% 3.13/1.07 % ------ iProver source info
% 3.13/1.07
% 3.13/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 3.13/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.13/1.07 % git: non_committed_changes: false
% 3.13/1.07
% 3.13/1.07 % ------ Parsing...
% 3.13/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.13/1.07
% 3.13/1.07 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.13/1.07
% 3.13/1.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.13/1.07 % ------ Proving...
% 3.13/1.07 % ------ Problem Properties
% 3.13/1.07
% 3.13/1.07 %
% 3.13/1.07 % clauses 10
% 3.13/1.07 % conjectures 10
% 3.13/1.07 % EPR 7
% 3.13/1.07 % Horn 10
% 3.13/1.07 % unary 8
% 3.13/1.07 % binary 0
% 3.13/1.07 % lits 16
% 3.13/1.07 % lits eq 0
% 3.13/1.07 % fd_pure 0
% 3.13/1.07 % fd_pseudo 0
% 3.13/1.07 % fd_cond 0
% 3.13/1.07 % fd_pseudo_cond 0
% 3.13/1.07 % AC symbols 0
% 3.13/1.07
% 3.13/1.07 % ------ Schedule dynamic 5 is on
% 3.13/1.07
% 3.13/1.07 % ------ no equalities: superposition off
% 3.13/1.07
% 3.13/1.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.13/1.07
% 3.13/1.07
% 3.13/1.07 % ------
% 3.13/1.07 % Current options:
% 3.13/1.07 % ------
% 3.13/1.07
% 3.13/1.07
% 3.13/1.07 %
% 3.13/1.07
% 3.13/1.07 % ------ Proving...
% 3.13/1.07 %
% 3.13/1.07
% 3.13/1.07 % SZS status Theorem for theBenchmark.p
% 3.13/1.07
% 3.13/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.13/1.07
% 3.13/1.07
%------------------------------------------------------------------------------